By default, Mechanic's activity log omits events that haven't performed any work yet. This means that, even if Mechanic's queueing up work for you, you might not see it right away.
To change this, open up your Mechanic account settings, using the "Manage settings" toward the end of your Mechanic homepage:
Then, disable the "Hide events that did nothing" setting.
When you return to your Mechanic homepage, you'll see every event that Mechanic has processed for you – even the ones that don't have any realized work yet.
If you still don't see anything in your activity log, it's possible that Shopify hasn't notified Mechanic of any events just yet. To illustrate, if you've set up a task that sends a follow-up email to customers a week after fulfillment, you won't see anything in your activity log until a new order fulfillment goes through. In this scenario, consider performing some test activity of your own, in Shopify, to trigger your task.
If you've run through all of the above and you're still not sure why no activity is showing, send us a message, and we'll help you out. :)